Logic Programming pair #487096326

details

property	value
status	complete
benchmark	p_nonlin.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	SGST06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.93736 seconds
cpu usage	8.23649
user time	7.83502
system time	0.401473
max virtual memory	3.7656868E7
max residence set size	768504.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

p(g)

w.r.t. the given Prolog program could successfully be proven:

(0) Prolog
(1) PrologToPiTRSProof [SOUND, 0 ms]
(2) PiTRS
(3) DependencyPairsProof [EQUIVALENT, 6 ms]
(4) PiDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) PiDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) PiDP
        (10) PiDPToQDPProof [SOUND, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) PiDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) PiDP
        (17) PiDPToQDPProof [SOUND, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) PiDP
        (22) PiDPToQDPProof [SOUND, 0 ms]
        (23) QDP
        (24) QDPQMonotonicMRRProof [EQUIVALENT, 61 ms]
        (25) QDP
        (26) DependencyGraphProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) UsableRulesProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) QReductionProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) PisEmptyProof [EQUIVALENT, 0 ms]
        (35) YES


----------------------------------------

(0)
Obligation:
Clauses:

p(cons(X, nil)).
p(cons(s(s(X)), cons(Y, Xs))) :- ','(p(cons(X, cons(Y, Xs))), ','(mult(X, Y, Z), p(cons(Z, Xs)))).
p(cons(0, Xs)) :- p(Xs).
sum(X, 0, X).
sum(X, s(Y), s(Z)) :- sum(X, Y, Z).
mult(X1, 0, 0).
mult(X, s(Y), Z) :- ','(mult(X, Y, W), sum(W, X, Z)).


Query: p(g)
----------------------------------------

(1) PrologToPiTRSProof (SOUND)
We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:

p_in_1: (b)

mult_in_3: (b,b,f)

sum_in_3: (b,b,f)

Transforming Prolog into the following Term Rewriting System:

Pi-finite rewrite system:
The TRS R consists of the following rules:

   p_in_g(cons(X, nil)) -> p_out_g(cons(X, nil))
   p_in_g(cons(s(s(X)), cons(Y, Xs))) -> U1_g(X, Y, Xs, p_in_g(cons(X, cons(Y, Xs))))
   p_in_g(cons(0, Xs)) -> U4_g(Xs, p_in_g(Xs))
   U4_g(Xs, p_out_g(Xs)) -> p_out_g(cons(0, Xs))
   U1_g(X, Y, Xs, p_out_g(cons(X, cons(Y, Xs)))) -> U2_g(X, Y, Xs, mult_in_gga(X, Y, Z))
   mult_in_gga(X1, 0, 0) -> mult_out_gga(X1, 0, 0)
   mult_in_gga(X, s(Y), Z) -> U6_gga(X, Y, Z, mult_in_gga(X, Y, W))
   U6_gga(X, Y, Z, mult_out_gga(X, Y, W)) -> U7_gga(X, Y, Z, sum_in_gga(W, X, Z))
   sum_in_gga(X, 0, X) -> sum_out_gga(X, 0, X)
   sum_in_gga(X, s(Y), s(Z)) -> U5_gga(X, Y, Z, sum_in_gga(X, Y, Z))
   U5_gga(X, Y, Z, sum_out_gga(X, Y, Z)) -> sum_out_gga(X, s(Y), s(Z))
   U7_gga(X, Y, Z, sum_out_gga(W, X, Z)) -> mult_out_gga(X, s(Y), Z)
   U2_g(X, Y, Xs, mult_out_gga(X, Y, Z)) -> U3_g(X, Y, Xs, p_in_g(cons(Z, Xs)))
   U3_g(X, Y, Xs, p_out_g(cons(Z, Xs))) -> p_out_g(cons(s(s(X)), cons(Y, Xs)))

The argument filtering Pi contains the following mapping:
p_in_g(x1)  =  p_in_g(x1)

cons(x1, x2)  =  cons(x1, x2)

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